Tools

"... Abstract. In this work the relation between Boolean Matrix Multipli-cation (BMM) and Context Free Grammar (CFG) parsing is shown. The first described approach, which is due to Valiant (1975), shows how CFG parsing can be reduced to Boolean Matrix Multiplication. Afterwards the reverse direction, i.e ..."

Abstract. In this work the relation between BooleanMatrixMultipli-cation (BMM) and Context Free Grammar (CFG) parsing is shown. The first described approach, which is due to Valiant (1975), shows how CFG parsing can be reduced to BooleanMatrixMultiplication. Afterwards the reverse direction, i

"... A classical topic in computer science is matrix multiplication and Boolean Matrix Multiplication in particular. Most papers studying these problems present worst case algorithms with running times O(n 2+ff ). For smaller ff these algorithms are rather complex and difficult to understand. As for s ..."

A classical topic in computer science is matrixmultiplication and BooleanMatrixMultiplication in particular. Most papers studying these problems present worst case algorithms with running times O(n 2+ff ). For smaller ff these algorithms are rather complex and difficult to understand

We present a new combinatorial algorithm for triangle finding and Booleanmatrixmultiplication that runs in Ô(n3 / log4 n) time, where the O ̂ notation suppresses poly(loglog) factors. This improves the previous best combi-natorial algorithm by Chan [4] that runs in Ô(n3 / log3 n) time. Our

"... this paper we restate the TAG parsing problem as a search problem and relate it to the well-known computational problem of Boolean matrix multiplication. This is done in such a way that time upper bounds for TAG parsing can be transferred to time upper bounds for the latter problem. More precisely, ..."

this paper we restate the TAG parsing problem as a search problem and relate it to the well-known computational problem of Booleanmatrixmultiplication. This is done in such a way that time upper bounds for TAG parsing can be transferred to time upper bounds for the latter problem. More precisely

"... A time-space tradeoff is established in the branching program model for the problem of computing the product of two n x n matrices over the semiring ((0, l}, V, A). It is a.ssumed that ea.ch element of each nxn input matrix is chosen independently to be 1 with probability n-ll2 and to be 0 with prob ..."

A time-space tradeoff is established in the branching program model for the problem of computing the product of two n x n matrices over the semiring ((0, l}, V, A). It is a.ssumed that ea.ch element of each nxn input matrix is chosen independently to be 1 with probability n-ll2 and to be 0

In 1975, Valiant showed that Booleanmatrixmultiplication can be used for parsing context-free grammars (CFGs), yielding the asympotically fastest (although not practical) CFG parsing algorithm known. We prove a dual result: any CFG parser with time complexity $O(g n^{3 - \epsilson})$, where $g

"... The quantum query complexity of Boolean matrix multiplication is typically studied as a function of the matrix dimension, n, as well as the number of 1s in the output, ℓ. We prove an upper bound of Õ(n √ ℓ) for all values of ℓ. This is an improvement over previous algorithms for all values of ℓ. On ..."

The quantum query complexity of Booleanmatrixmultiplication is typically studied as a function of the matrix dimension, n, as well as the number of 1s in the output, ℓ. We prove an upper bound of Õ(n √ ℓ) for all values of ℓ. This is an improvement over previous algorithms for all values of ℓ

"... Valiant showed that Boolean matrix multiplication (BMM) can be used for CFG parsing. We prove a dual result: CFG parsers running in time $O(|G||w|^{3 - \myeps})$ on a grammar $G$ and a string $w$ can be used to multiply $m \times m$ Boolean matrices in time $O(m^{3 - \myeps/3})$. In the process we a ..."

Valiant showed that Booleanmatrixmultiplication (BMM) can be used for CFG parsing. We prove a dual result: CFG parsers running in time $O(|G||w|^{3 - \myeps})$ on a grammar $G$ and a string $w$ can be used to multiply $m \times m$ Boolean matrices in time $O(m^{3 - \myeps/3})$. In the process we

"... We present new quantum algorithms for Boolean Matrix Multiplication in both the time complexity and the query complexity settings. As far as time complexity is concerned, our results show that the product of two n × n Boolean matrices can be computed on a quantum computer in time Õ(n 3/2 + nℓ 3/4), ..."

We present new quantum algorithms for BooleanMatrixMultiplication in both the time complexity and the query complexity settings. As far as time complexity is concerned, our results show that the product of two n × n Boolean matrices can be computed on a quantum computer in time Õ(n 3/2 + nℓ 3

"... Small sample spaces with almost independent random variables are applied to design efficient sequential deterministic algorithms for two problems. The first algorithm, motivated by the attempt to design efficient algorithms for the All Pairs Shortest Path problem using fast matrix multiplication, so ..."

Small sample spaces with almost independent random variables are applied to design efficient sequential deterministic algorithms for two problems. The first algorithm, motivated by the attempt to design efficient algorithms for the All Pairs Shortest Path problem using fast matrixmultiplication